When wrapping paper for low ignition propensity cigarettes is produced, a web (paper) is applied with a combustion inhibitor. The web is then dried, smoothed to remove wrinkles, and wound into a roll (see Patent Document 1, by way of example). Such drying is carried out using a drying device, and the web dries as it is conveyed at a constant speed through the drying device. However, the web shrinks as it becomes dry, and thus if the web is conveyed at a constant speed, tearing of the web, reduction in the width of the web due to lengthwise pull or formation of fine wrinkles that are difficult to remove is liable to be caused as the web travels downstream.